Method and apparatus for channel encoding and decoding in a communication system using a low-density parity check code

ABSTRACT

A method is provided for channel encoding in a communication system using an LDPC code. The method includes encoding input bits using a BCH code, shortening bits of the encoded input bits according to a number of bit groups to be shortened and an order among a plurality of orders according to which the bit groups are shortened, wherein the number of bit groups to be shortened is based on a number of bits to be shortened, which is based on a number of the encoded input bits, encoding information bits including the encoded input bits and the shortened one or more bits, using an LDPC code to generate parity bits, puncturing bits in the parity bits based on a puncturing parameter among puncturing parameters, and transmitting a signal generated from the encoded information bits based on the punctured bits. The plurality of orders being based on the puncturing parameters and including first and second orders.

PRIORITY

This application is a Continuation application of U.S. patentapplication Ser. No. 14/842,210 which was filed in the U.S. Patent andTrademark Office on Sep. 1, 2015, which is a Divisional application ofU.S. patent application Ser. No. 14/164,870, which was filed in the U.S.Patent and Trademark Office on Jan. 27, 2014, issued as U.S. Pat. No.9,525,433 on Dec. 20, 2016, which is a Divisional application of U.S.patent application Ser. No. 12/962,262, filed on Dec. 7, 2010, issued asU.S. Pat. No. 8,689,093 on Apr. 1, 2014, which claims priority under 35U.S.C. § 119(a) to a Korean Patent Application filed in the KoreanIntellectual Property Office on Dec. 7, 2009 and assigned Serial No.10-2009-0120572, the entire content of each which is incorporated hereinby reference.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates generally to a communication system usinga Low-Density Parity Check (LDPC) code, and more particularly, to achannel encoding/decoding method and apparatus for supporting variouscodeword lengths or code rates using a given LDPC code.

2. Description of the Related Art

In wireless communication systems, link performances are significantlydegraded by various noises, fading of channels, and Inter-SymbolInterference (ISI). Therefore, to realize high-speed digitalcommunication systems requiring high data throughput and reliability,such as a next-generation mobile communication system, a digitalbroadcasting system, and a mobile Internet system, it is important todevelop technologies for coping with the noises, fading, and ISI.Recently, error-correcting codes have been studied for improvingcommunication reliability by efficiently restoring informationdistortion.

An LDPC code, which was first introduced as a typical example of theerror-correcting code by Gallager in 1960s, has been long forgotten dueto its implementation complexity far exceeding the then technology.However, the LDPC code was restudied in late 1990s, proving that theLDPC code has performance close to Shannon's channel capacity, ifdecoded by sum-product algorithm-based iterative decoding on a Tannergraph corresponding to the LDPC code. Therefore, the LDPC code is nowagain being used or considered for use in various systems.

The LDPC code can be commonly defined by a parity check matrix, and canbe represented using a bipartite graph called a Tanner graph. Thebipartite graph includes two different types of vertexes, which arecalled variable nodes and check nodes. The variable nodes correspond toencoded bits on a one-to-one basis, and the check nodes representalgebraic relationships between the encoded bits.

FIG. 1 illustrates an example of a parity check matrix H₁ of an LDPCcode having four rows and eight columns. Referring to FIG. 1, the paritycheck matrix H₁ generates a codeword with a length of 8, because it haseight columns.

FIG. 2 illustrates a Tanner graph corresponding to the parity checkmatrix H₁ of the LDPC code, as illustrated in FIG. 1.

Referring to FIG. 2, the Tanner graph includes eight variable nodes x₁202, x₂ 204, x₃ 206, x₄ 208, x₅ 210, x₆ 212, x₇ 214, and x₈ 216, andfour check nodes 218, 220, 222, and 224. An i-th column and a j-th rowin the parity check matrix H₁ correspond to a variable node x_(i) and aj-th check node, respectively. A value of 1, i.e., a non-zero value, atthe point where an i-th column and a j-th row cross in the parity checkmatrix H₁ indicate that an edge exists between the variable node x_(i)and the j-th check node on the Tanner graph, as illustrated in FIG. 2.

In the Tanner graph, a degree of each of the variable nodes and thecheck nodes means the number of edges connected thereto, and isidentical to the number of entries, which are not zero (0) in columns orrows corresponding to their associated nodes in the parity check matrix.For example, in FIG. 2, degrees of the variable nodes x₁ 202, x₂ 204, x₃206, x₄ 208, x₅ 210, x₆ 212, x₇ 214, and x₈ 216 are 4, 3, 3, 3, 2, 2, 2,and 2, respectively, and degrees of the check nodes 218, 220, 222, and224 are 6, 5, 5, and 5, respectively. As mentioned above, the number ofnon-zero entries in columns in the parity check matrix H₁ of FIG. 1,which correspond to the variable nodes of FIG. 2, are equal to the abovedegrees 4, 3, 3, 3, 2, 2, 2, and 2 in order, and the number of non-zeroentries in rows in the parity check matrix H₁ of FIG. 1, whichcorrespond to the check nodes of FIG. 2, are identical to the abovedegrees 6, 5, 5, and 5 in order.

To represent a degree distribution for nodes of an LDPC code, it isassumed that a ratio of the number of variable nodes with a degree i tothe total number of variable nodes is represented by f_(i) and a ratioof the number of check nodes with a degree j to the total number ofcheck nodes is represented by g_(j). For example, for the LDPC codecorresponding to FIGS. 1 and 2, f₂= 4/8, f₃=⅜, and f₄=⅛, and f_(i)=0 fori≠2, 3, 4; and g₅=¾ and g₆=¼, and g_(j)=0 for j≠5, 6. Assuming that alength (i.e., the number of columns) of an LDPC code is N and the numberof rows is N/2, a density of non-zero entries in the entire parity checkmatrix having the above degree distribution is calculated using Equation(1) below.

$\begin{matrix}{\frac{{2f_{2}N} + {3f_{3}N} + {4f_{4}N}}{N \cdot {N/2}} = \frac{5.25}{N}} & (1)\end{matrix}$

In Equation (1), increasing N decreases the density of a weight of 1 inthe parity check matrix. For an LDPC code, because its length N isinverse proportional to the density of non-zero entries, an LDPC codewith a large N has a very low density of non-zero entries. The phrase‘low density’ in the name LDPC code was derived from this principle.

FIG. 3 is a diagram illustrating a conventional LDPC encoding process.

Referring to FIG. 3, the number of bits input to an LDPC encoder 310 is,for example, K₁=16, and information bits are represented as, forexample, {right arrow over (u)}={u₀,u₁, . . . , u₁₅}. Herein, the bitsinput to the LDPC encoder 310 will be referred to individually asinformation bits or collectively as an information word.

The LDPC encoder 310 generates parity bits, and generates an LDPCcodeword {right arrow over (c)}=({right arrow over (u)}, {right arrowover (p)}) by adding the generated parity bits to the input informationbits as illustrated in FIG. 3. A process in which the LDPC encoder 310adds parity bits to information bits using the parity check matrix isreferred to as an LDPC encoding process.

Because an LDPC code is defined by a parity check matrix, a given systemstores the parity check matrix in order to apply the LDPC code.Generally, to store an LDPC code, position information of a weight of 1in the parity check matrix is stored. However, because a codeword lengthof an LDPC code used in the actual system ranges from hundreds of bitsto hundreds of thousands of bits, the memory required to store theposition information of a weight of 1 can become very large in capacityif the codeword length of the LDPC code is very long.

To overcome these shortcomings, many studies have been conducted on LDPCcodes with various parity check matrixes having specific structures. Fora parity check matrix having a specific structure, because positions ofa weight of 1 are limited in its parity check matrix according to aspecific condition, the positions of a weight of 1 can be stored moreefficiently.

FIG. 4 is a diagram illustrating a parity check matrix having thespecific structure.

Referring to FIG. 4, N₁ represents a length of an LDPC codeword, whichis equal to a length of its parity check matrix. K₁ represents a lengthof an information word (or the number of information bits), which isequal to a length of an information part of the parity check matrix, and(N₁−K₁) represents a length of parity bits, which is equal to a lengthof a parity part of the parity check matrix. Integers M₁ and q aredetermined so as to meet q=(N₁−K₁)/M₁. K₁/M₁ is also an integer.

In the parity check matrix of FIG. 4, positions of a weight of 1 in aK₁-th column to an (N₁−1)-th column, which are a part corresponding tothe parity bits, have a dual diagonal structure. Therefore, it can beunderstood that degrees of columns corresponding to the parity bits areall 2, except for a degree of the (N₁−1)-th column, which is 1.

Referring to FIG. 4, in the parity check matrix, a structure of a 0-thcolumn to a (K₁−1)-th column, which corresponds to an information part,can be made according to the following rules:

Rule 1: In the parity check matrix, a total of K₁/M₁ column groups aregenerated by grouping K₁ columns corresponding to an information wordinto a plurality of groups each including M₁ columns. Columns in eachcolumn group are generated according to Rule 2 below.

Rule 2: First, positions of 1 in a 0-th column in an i-th (i=1, . . . ,K₁/M₁) column group are determined. Second, assuming that a degree of a0-th column in each i-th column group is represented by D_(i), ifpositions of rows with 1 are R_(i,0) ⁽¹⁾, R_(i,0) ⁽²⁾, . . . , R_(i,0)^((D) ^(i) ⁾, then positions R_(i,j) ^((k)) (k=1, 2, . . . , D_(i)) ofrows with 1 in a j-th (j=1, 2, . . . , M₁−1) column in an i-th columngroup are defined as shown in Equation (2) below.

R _(i,j) ^((k)) =R _(i,(j-1)) ^((k)) +q mod(N ₁ −K ₁)  (2)

-   -   k=1, 2, . . . , D_(i), i=1, . . . , K₁/M₁, j=1, . . . , M₁−1

According to Rules 1 and 2, it is noted that degrees of columns in ani-th (i=1, . . . , K₁/M₁) column group are all equal to D_(i). Now,

As a more detailed example, for N₁=30, K₁=15, M₁=5 and q=3, positioninformation of rows with 1 in a 0-th column in each of three columngroups may be represented in the following three sequences. Thesesequences are referred to as “weight-1 position sequences”.

-   -   R_(1,0) ⁽¹⁾=1, R_(1,0) ⁽²⁾=2, R_(1,0) ⁽³⁾=8, R_(1,0) ⁽⁴⁾=10,    -   R_(2,0) ⁽¹⁾=0, R_(2,0) ⁽²⁾=9, R_(2,0) ⁽³⁾=13,    -   R_(3,0) ⁽¹⁾=0, R_(3,0) ⁽²⁾=14.

As to the weight-1 position sequences for positions of rows with 1 in a0-th column in each column group, only their sequences are alsorepresented on a column group basis as follows, for convenience.

-   -   1 2 8 10    -   0 9 13    -   0 14

That is, the i-th weight-1 position sequence sequentially representsposition information of rows with 1 in an i-th column group.

FIG. 5 is a diagram illustrating an example of a parity check matrix ofan LDPC code. Specifically, the parity check matrix illustrated in FIG.5 is generated by constructing a parity check matrix using theinformation corresponding to the above detailed example, and Rules 1 and2.

To apply an LDPC code to an actual communication system, the LDPC codeshould be generated in consideration of a required data rate in thecommunication system. In particular, not only in an adaptivecommunication system employing Hybrid Automatic Retransmission Request(HARQ) and Adaptive Modulation and Coding (AMC), but also in acommunication system supporting various broadcast services, LDPC codeshaving various codeword lengths are required to support various datarates required by the systems.

However, in order to support LDPC codes having various codeword lengthsor code rates, a high-capacity memory is required to store parity checkmatrixes corresponding to different codeword lengths or code rates. Inparticular, an increase in the number of types of the supported codewordlengths or code rates also lead to an increase in the required memorycapacity, thereby reducing the system efficiency. Therefore, there is aneed for more efficiently supporting a variety of codeword lengths orcode rates using a given, existing parity check matrix, withoutgenerating new parity check matrixes corresponding to different codewordlengths or code rates.

SUMMARY

The present invention is designed to address at least theabove-mentioned problems and/or disadvantages and to provide at leastthe advantages described below.

Accordingly, an aspect of the present invention is to provide a channelencoding and decoding method and apparatus for generating LDPC codeshaving different codeword lengths and code rates by shortening orpuncturing a given parity check matrix in a communication system usingan LDPC code.

Another aspect of the present invention is to provide a channel encodingand decoding method and apparatus for determining a shortening patternconsidering a number of shortened bits and a number of punctured bits ina communication system using an LDPC code.

Another aspect of the present invention is to provide a channel encodingand decoding method and apparatus for ensuring optimal performance byconsidering a specific structure in a communication system using an LDPCcode having the specific structure.

In accordance with an aspect of the present invention, a method isprovided for channel encoding in a communication system usinglow-density parity check (LDPC) codes having different codeword lengthsand a parity check matrix by performing at least one of shortening orpuncturing. The method includes encoding input bits using aBose-Chaudhuri-Hocquenghem (BCH) code; shortening one or more bits ofthe encoded input bits according to a number of bit groups to beshortened and an order among a plurality of orders according to whichthe bit groups are shortened, wherein the number of bit groups to beshortened is based on a number of bits to be shortened which is based ona number of the encoded input bits; encoding information bits includingthe encoded input bits and the shortened one or more bits, using an LDPCcode to generate parity bits; puncturing one or more bits in the paritybits based on a puncturing parameter among puncturing parameters; andtransmitting a signal that is generated from the encoded informationbits based on the punctured one or more bits. The plurality of ordersare based on the puncturing parameters and include a first order and asecond order that is different from the first order.

In accordance with another aspect of the present invention, an apparatusis provided for channel encoding in a communication system usinglow-density parity check (LDPC) codes having different codeword lengthsand a parity check matrix by performing at least one of shortening orpuncturing. The apparatus includes at least one processor configured toencode input bits using a Bose-Chaudhuri-Hocquenghem (BCH) code, shortenone or more bits of the encoded input bits according to the of bitgroups to be shortened and an order among a plurality of ordersaccording to which the bit groups are shortened, wherein the number ofbit groups to be shortened is based on a number of bits to be shortenedwhich is based on a number of the encoded input bits, encode informationbits including the encoded input bits and the shortened one or more bitsusing an LDCP code to generate parity bits, and puncture one or morebits in the parity bits based on a puncturing parameter among puncturingparameters LDPC-encoded information bits; and a transmitter configuredto transmit a signal that is generated from the encoded information bitsbased on the punctured one or more bits. The plurality of orders arebased on puncturing the parameters and include a first order and asecond order that is different from the first order.

In accordance with another aspect of the present invention, a method isprovided for channel decoding in a communication system usinglow-density parity check (LDPC) codes having different codeword lengthsand a parity check matrix by performing at least one of shortening orpuncturing. The method includes receiving, from a transmitter, a signalthat is generated from encoded information bits, based on punctured oneor more bits; and decoding data in the received signal. The encodedinformation bits are generated by encoding, using an LDPC code togenerate parity bits, information bits including encoded input bitsusing a Bose-Chaudhuri-Hocquenghem (BCH) code and shortened one or morebits. The punctured one or more bits are punctured in the parity bitsbased on a puncturing parameter among puncturing parameters. The one ormore bits are shortened according to a number of bit groups to beshortened and an order among a plurality of orders according to whichthe bit groups are shortened. The number of bit groups to be shortenedis based on a number of bits to be shortened, which is based on a numberof the encoded input bits. The plurality of orders are based on thepuncturing parameters and include a first order and a second order thatis different from the first order.

In accordance with another aspect of the present invention, an apparatusis provided for channel decoding in a communication system usinglow-density parity check (LDPC) codes having different codeword lengthsand a parity check matrix by performing at least one of shortening orpuncturing. The apparatus includes a receiver configured to receive,from a transmitter, a signal that is generated from encoded informationbits, based on punctured one or more bits; and at least one processorconfigured to decode data in the received signal. The encodedinformation bits are generated by encoding, using an LDPC code togenerate parity bits, information bits including encoded input bitsusing a Bose-Chaudhuri-Hocquenghem (BCH) code and shortened one or morebits. The punctured one or more bits are punctured in the parity bitsbased on a puncturing parameter among puncturing parameters. The one ormore bits are shortened according to a number of bit groups to beshortened and an order among a plurality of orders according to whichthe bit groups are shortened. The number of bit groups to be shortenedis based on a number of bits to be shortened, which is based on a numberof the encoded input bits. The plurality of orders are based on thepuncturing parameters and include a first order and a second order thatis different from the first order.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features, and advantages of certainembodiments of the present invention will be more apparent from thefollowing description taken in conjunction with the accompanyingdrawings, in which:

FIG. 1 is a diagram illustrating an example of a parity check matrix ofan LDPC code with a length of 8;

FIG. 2 is a diagram illustrating an exemplary Tanner graph of a paritycheck matrix of an LDPC code with a length of 8;

FIG. 3 is a block diagram illustrating an LDPC encoding process;

FIG. 4 is a diagram illustrating a structure of a parity check matrix;

FIG. 5 is a diagram illustrating an example of a parity check matrix ofan LDPC code;

FIG. 6 is a block diagram illustrating a transceiver in a communicationsystem using an LDPC code;

FIG. 7 is a flowchart illustrating a shortening process in acommunication system using an LDPC code;

FIG. 8 is a diagram illustrating an information part of an LDPC code;

FIG. 9 is a conceptual diagram illustrating a process of shortening anLDPC code on a column group basis;

FIG. 10 is a diagram illustrating criteria for determining shorteningpatterns depending on systems, according to an embodiment of the presentinvention;

FIG. 11 is a flowchart illustrating a transmission operation in atransmission apparatus according to an embodiment of the presentinvention;

FIG. 12 is a block diagram illustrating an LDPC code-based transmissionapparatus utilizing a shortening method according to an embodiment ofthe present invention;

FIG. 13 is a block diagram illustrating an LDPC code-based receptionapparatus utilizing a shortening method according to an embodiment ofthe present invention; and

FIG. 14 is a flowchart illustrating a reception operation in a receptionapparatus according to an embodiment of the present invention.

Throughout the drawings, the same drawing reference numerals will beunderstood to refer to the same elements, features, and structures.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE PRESENT INVENTION

Various embodiments of the present invention will now be described indetail with reference to the accompanying drawings. In the followingdescription, specific details such as detailed configuration andcomponents are merely provided to assist the overall understanding ofthese embodiments of the present invention. Therefore, it should beapparent to those skilled in the art that various changes andmodifications of the embodiments described herein can be made withoutdeparting from the scope and spirit of the present invention. Inaddition, descriptions of well-known functions and constructions areomitted for clarity and conciseness.

In accordance with an embodiment of the present invention a method forsupporting LDPC codes having a variety of codeword lengths or code ratesusing a parity check matrix in a specific form is provided. Inaccordance with another embodiment of the present invention an apparatussupporting various codeword lengths or code rates in a communicationsystem that encodes an LDPC code using a parity check matrix in aspecific form is provided.

FIG. 6 is a block diagram illustrating a transceiver in a communicationsystem using an LDPC code.

Referring to FIG. 6, a message u to be sent is input to an LDPC encoder611 in a transmitter 610. The LDPC encoder 611 transfers, to a modulator613, a signal or a codeword c that is obtained by encoding the inputmessage u. The modulator 613 modulates the codeword c and transmits amodulated signal s to a receiver 630 over a channel 620. A demodulator631 in the receiver 630 demodulates a signal r received from thetransmitter 610, and outputs a demodulated signal x to an LDPC decoder633. The LDPC decoder 633 decodes the demodulated signal x to estimatean estimate u of the message.

More specifically, the LDPC encoder 611 generates the codeword c byselecting a parity check matrix corresponding to a codeword length orcode rate required by a communication system using a preset scheme.Particularly, an embodiment of the present invention provides a methodin which the LDPC encoder 611 can support various codeword lengths orcode rates without the need to store additional information.

In accordance with an embodiment of the present invention, shorteningand/or puncturing methods are used to supporting various codewordlengths or code rates.

The shortening method limits a value of a specific bit or a specificpart of an information word to ‘0’ or ‘1’. That is, the shorteningmethod either does not use a specific part, or only uses a specific partof a given parity check matrix. For a better understanding of theshortening method, reference will be made in detail to the parity checkmatrix of the LDPC code illustrated in FIG. 4.

The parity check matrix of the LDPC code illustrated in FIG. 4 is N₁ inits total length, an information part representing a front part of theparity check matrix corresponds to information bits (i₀,i₀, . . . ,i_(K) ₁ ⁻¹) with a length of K₁, and a parity part representing a rearpart of the parity check matrix corresponds to parity bits (p₀,p₀, . . ., p_(N) ₁ _(K) ₁ ⁻¹) with a length of N₁−K₁. Commonly, information bitsfreely have a value of 0 and 1, but in the shortening method, values ofinformation bits in a specific part to be shortened are limited, asdescribed above.

For example, shortening N_(s) information bits i₀ to i_(N) _(s) ⁻¹commonly means i₀=i₁= . . . =i_(N) ₁ ⁻¹=0. That is, shortening isperformed by limiting values of N_(s) information bits i₀ to i_(N) _(s)⁻¹ to 0. Alternatively, shortening may be performed by not using N_(s)columns of an information part in the parity check matrix illustratedFIG. 3, as described above. That is, the shortening method of limitingvalues of specific information bits to 0 may be implemented by ashortening method of removing or not using columns corresponding to theinformation bits whose values are limited to 0, in the parity checkmatrix. Therefore, the shortening method of limiting values of specificinformation bits or a bit group to 0 may be replaced with the shorteningmethod of removing corresponding columns or column group in the paritycheck matrix. As described above, information bits correspond to aninformation part of a parity check matrix, and a bit group is a group ofinformation bits corresponding to a column group in the parity checkmatrix.

In the following description, even though any the various embodiments ofthe present invention may be described with reference to only one of theshortening methods, the other shortening method would also be available.Through these shortening methods, because position information aboutshortened information bits may be equally shared or generated by atransmitter and a receiver during system setting, even though thetransmitter does not transmit shortened information bits, the receivermay perform decoding, knowing values of information bits in thepositions of the shortened information bits.

By using the shortening method, because a length of a codeword actuallytransmitted by a transmitter is N₁−N_(s) and a length of an actualinformation word is K₁−N_(s), a code rate becomes (K₁−N_(s))/(N₁−N_(s)),which is less than the first given code rate K₁/N₁.

A puncturing method may be generally applied to both information bitsand parity bits. While both the puncturing method and the shorteningmethod shorten a codeword length, the puncturing method, unlike theshortening method, does not limit values of specific bits. Instead, thepuncturing method simply does not transmit specific information bits, orspecific bits or a specific part among generated parity bits, so theyundergo erasure processing in a receiver. In other words, simply nottransmitting N_(p) bits in predetermined positions in a generated LDPCcode with a length of N₁ is equivalent to transmitting an LDPC code witha length of N₁−N_(p). Because columns corresponding to punctured bits ina parity check matrix are used intact in a decoding process, thepuncturing method is different from the shortening method.

Because position information about punctured bits may be equally sharedor estimated by a transmitter and a receiver during system setting, thereceiver may simply perform erasure processing on the punctured bitsduring decoding.

FIG. 7 is a flow chart illustrating a shortening process in acommunication system using an LDPC code, which is applied to the presentinvention.

In step 701, an LDPC encoder extracts information about a parity checkmatrix for shortening. The parity check matrix information may be atleast one of a stored parity check matrix, a part of a parity checkmatrix, and parameters of a parity check matrix, e.g., information abouta weight-1 position sequence, a length of or the number of column groupsof a parity check matrix, etc. The LDPC encoder determines (K₁-K₂)information bits to be obtained by shortening in step 703, anddetermines the number of bit groups or column groups for shortening instep 705. In step 707, the LDPC encoder performs shortening according toat least one of shortening patterns as defined in Tables 2 and 3 below.In accordance with an embodiment of the present invention, theshortening patterns defined in Tables 2 and 3 are determined consideringa ratio of a number of bits to be shortened to a number of bits to bepunctured.

An information part of the parity check matrix includes a plurality ofcolumn groups, e.g., K₁/M₁=3, as illustrated in FIG. 5. In a paritycheck matrix of an LDPC code, because columns correspond to informationbits of the LDPC code on a one-to-one basis, the column groupcorresponds to a specific bit group of information bits.

FIG. 8 is a diagram illustrating an information part of an LDPCcodeword.

Referring to FIG. 8, an LDPC codeword may be generated by beingconcatenated to a Bose-Chaudhuri-Hocquenghem (BCH) code. That is, BCHcoding (or BCH outer coding) is performed by adding a BCH parity 835 toan information word 833 (the information word 833 can be referred to asBCH information word for separation from LDPC information word 831), andLDPC encoding (or LDPC inner coding) is performed by adding an LDPCparity to the result obtained by adding the BCH parity 835 to the BCHinformation word 833. The result of adding a BCH parity to theinformation word 833 is referred to as an LDPC information word 831.Therefore, as illustrated in FIG. 8, the LDPC information word 831 of anLDPC code may be subdivided into a part corresponding to the BCHinformation word 833 and a part corresponding to the BCH parity 835.

Referring to FIG. 8, a length of the BCH parity 835 corresponding to atail end of the last (K₁/M₁−1)-th column group in the parity checkmatrix of an LDPC code is N_(BCH_Parity), and a length of the BCHinformation word 833 is K₁−N_(BCH_Parity). Because the BCH parity 835 isdetermined by the BCH information word 833, a length of an informationword that is actually adjustable in a system employing an LDPC encodingmethod, is K₁−N_(BCH_Parity). Therefore, shortening cannot be applied tothe BCH parity bits 835 with a length of N_(BCH_Parity). When shorteningcannot be applied to the N_(BCH_Parity) parity bits, a (K₁/M₁−1)-thcolumn group or bit group may be defined to apply shortening, except forthe N_(BCH_Parity) columns or bits therefrom.

Because the LDPC code using a parity check matrix having theabove-described specific structure has a special structure in units ofcolumn groups or corresponding bit groups, it is preferable to performshortening on a bit or column group basis to achieve superiorperformance when application of shortening is required.

FIG. 9 illustrates an example of shortening an LDPC code on a bit groupbasis. In FIG. 9, hatched parts 910 represent bits to be shortened.

If the number of bits to be shortened is determined, a first specificbit group is shortened according to a predetermined order. In FIG. 9, athird bit group 914 is shortened for the first time.

If there are more bits to be shortened, a predetermined second specificbit group is shortened overall. In FIG. 9, a (K₁/M₁−2)-th bit group 916shortened for the second time.

If there are more bits to be shortened, a predetermined third specificbit group is shortened overall. In FIG. 9, a (K₁/M₁−3)-th bit group 915is shortened for the third time.

This process is continuously repeated, and if the number of remainingbits to be shortened is less than a size M₁ of one bit group, a part ofthe bit group is shortened, completing the shortening process. In FIG.9, a part of a second bit group 913 is shortened for the last time.

An order of bit or column groups to be shortened should be determined inadvance, for shortening on a bit or column group basis. However, if bothshortening and puncturing should be applied in a given communicationsystem, the order of bit or column groups to be shortened, providingsuperior performance, may be different disadvantageously, depending onthe length of punctured parity bits. If puncturing is applied to paritybits, connectivity between punctured parity bits and information bitsaffects decoding performance, and their connection properties varyaccording to the number of punctured bits. For example, information bitsmost connected to punctured parity bits have a very high performancedegradation possibility, and such information bits may be changeddepending on the number of punctured parity bits. That is, positions ofinformation bits having a high performance degradation possibility arecontinuously changed according to the number of punctured parity bits.

Accordingly, when both shortening and puncturing are applied, theoptimal order of bit or column groups to be shortened may changeaccording to the length of bits to be punctured.

In accordance with an embodiment of the present invention, a patternhaving the best theoretical performance is determined through densityevolution analysis according to a predetermined ratio of shortening topuncturing, in order to determine the optimal order of bit or columngroups to be shortened, when both shortening and puncturing are appliedin an arbitrary system utilizing an LDPC code. Density evolutionanalysis may be applied by performing erasure processing on puncturedbits. The best degree distribution of an information part is calculated,and a shortening pattern satisfying the calculated degree distributionis calculated. If there are several shortening patterns satisfying thedegree distribution, a pattern having the best performance is selectedthrough computational experimentation.

An LDPC code with N₁=16200, K₁=3240, M₁=360, and q=36 will be consideredto describe application of an efficient shortening process using anexcellent shortening pattern obtained by the above process of selectinga shortening pattern. The LDPC code has the following weight-1 positionsequences:

-   -   6295 9626 304 7695 4839 4936 1660 144 11203 5567 6347 12557    -   10691 4988 3859 3734 3071 3494 7687 10313 5964 8069 8296 11090    -   10774 3613 5208 11177 7676 3549 8746 6583 7239 12265 2674 4292    -   11869 3708 5981 8718 4908 10650 6805 3334 2627 10461 9285 11120    -   7844 3079 10773    -   3385 10854 5747    -   1360 12010 12202    -   6189 4241 2343    -   9840 12726 4977

The sequence of an i-th row sequentially represents position informationof rows with 1 in an i-th column group. Therefore, the LDPC codeincludes nine column groups and a length of an information word of theLDPC code is 9×360=3240. Once a length of a codeword or an informationword to be obtained by applying shortening or puncturing is determined,an optimized shortening pattern can be calculated.

When an LDPC code is generated by being concatenated to a BCH code,shortening cannot be applied to a part corresponding to BCH parity bitsin an information word of the LDPC code. The BCH parity bits correspondto a tail end of the last (K₁/M₁−1)-th column group in the informationword of the LDPC code, and a length thereof is represented byN_(BCH_Parity). A length of a BCH information word is K₁−N_(BCH_Parity),and represented by K_(BCH). In addition, because BCH parity bits aredetermined by a BCH information word, a BCH information word is actuallyadjustable in a system employing an LDPC encoding method, and its lengthis K_(BCH).

Detailed examples of a shortening process and shortening patterns for anLDPC code with N₁=16200 and K₁=3240 are shown in Tables 1 to 3 below,wherein K_(2,BCH) and K_(2,LDPC) represent a length of a BCH informationword and a length of an LDPC information word after undergoingshortening, respectively. In Table 1, key parameters are changeableaccording to requirements of the system, and Tables 2 and 3 are alsochangeable according to the change of Table 1.

TABLE 1 Key N₁=16200, K₁=3240, K_(BCH)=3072, N_(BCH)_Parity=168,Parameters M₁=360, q=36 Step 1) A value of m is defined as followsaccording to a value of K_(2,BCH) . 1) m = K₁/M₁ − 1 for 0 < K_(2,BCH) ≤M₁ (or N_(BCH)_Parity < K_(2,LDPC) ≤ M₁ + N_(BCH)_{dot over ( )}Parity).${\left. 2 \right)\mspace{14mu} {Otherwise}},{m = {\left\lfloor \frac{K_{BCH} - K_{2,{BCH}}}{M_{1}} \right\rfloor.}}$Step 2) 1) π(0) -th, π(1) -th, ... , and π(m − 1) -th bit or columngroups are all shortened, where π(·) represents a sequence meaning ashortening pattern, and is selected from Tables 2 and 3 below accordingto a ratio of the number of bits to be shortened to the number of bitsto be punctured, or to a code rate. 2) When shortening is applied to a(K₁/M₁ − 1)-th bit or column group, if BCH parity bits with a length ofN_(BCH)_Parity or their corresponding columns are included in the group,shortening cannot be applied to the BCH parity bits or columns. Step3) 1) If m = K₁/M₁ − 1 , shortening is applied to (M₁ − K_(2,BCH)) bitsor columns in a π(K₁/M₁ − 1) -th bit or column group. 2) If m ≠ K₁/M₁ −1, shortening is applied to (K_(BCH) − K_(2,BCH) − m · M₁) bits orcolumns in a π(m) -th bit or column group. 3) When shortening is appliedto a (K₁/M₁ − 1)-th bit or column group, if BCH parity bits with alength of N_(BCH)_Parity or their corresponding columns are included inthe group, shortening cannot be applied to the BCH parity bits orcolumns.

TABLE 2 Number of information bits to be shortened/number of bits to bepunctured = 4/15, 3/11 π(0) π(1) π(2) π(3) π(4) π(5) π(6) π(7) π(8) 7 63 5 2 4 1 8 0

TABLE 3 Number of information bits to be shortened/number of bits to bepunctured = 2/7 π(0) π(1) π(2) π(3) π(4) π(5) π(6) π(7) π(8) 7 3 6 5 2 41 8 0

If a ratio of a number of bits to be shortened to a number of bits to bepunctured is 4/15 or 3/11, an LDPC encoder performs shortening on7^(th), 6^(th), 3^(rd), 5^(th), 2^(nd), 4^(th), 1^(st), 8^(th), and0^(th) groups in order, as defined in Table 2. However, if a length ofthe LDPC code is 16200, a length of the information word is 3240, and aratio of the number of bits to be shortened to the number of bits to bepunctured is 2/7, the LDPC encoder performs shortening on 7^(th),3^(rd), 6^(th), 5^(th), 2^(nd), 4^(th), 1^(st), 8^(th), and 0^(th)groups in order, as defined in Table 3.

Referring to Step 2) in Table 1, a different shortening pattern isselected depending on a ratio of a number of bits to be shortened to anumber of bits to be punctured, and criteria for determining shorteningpatterns may be expressed in various forms according to the systems.That is, a specific region in a frame has a specific ratio of the numberof bits to be shortened to the number of bits to be punctured. Ifanother region, or a part of the another region has a ratio of a numberof bits to be shortened to a number of bits to be punctured, which isdifferent from the specific ratio, a different shortening pattern may beselected for the another region, or the part of the another region,according to the specific region instead of the ratio.

FIG. 10 illustrates examples of criteria for determining shorteningpatterns depending on systems, according to an embodiment of the presentinvention.

Referring to FIG. 10, a specific region in a frame is used for signalingin, for example, Digital Video Broadcasting-Second GenerationTerrestrial (DVB-T2), DVB-Satellite Second Generation (DVB-S2),DVB-Cable Second Generation (DVB-C2) systems or a DVB-Next GenerationHandheld (DVB-NGH) system, which is currently under standardization. Inparticular, specific signaling regions L1-post configuration 1010 and1012 may be different from other signaling regions L1-pre 1014 and 1016and L1-post dynamic 1018 and 1020 in terms of the ratio of the number ofshortened bits to the number of punctured bits. In this case, the otherregions, i.e., L1-pre 1014 and 1016 and L1-post Dynamic 1018 and 1020,being different from the specific regions L1-post configuration 1010 and1012, or some regions, e.g., only L1-post Dynamic 1018 and 1020, of theother regions may use different shortening patterns. If a ratio of anumber of bits to be shortened to a number of bits to be punctured isdifferent, a code rate may be different. Therefore, if a code rate isdifferent, a different shortening pattern may be used.

Tables 2 and 3 represent positions of groups to be shortened, orrepresent an order of groups to be shortened. That is, a shorteningpattern π is used to indicate which bit group or column group should beshortened, and a shortening pattern π represents π(0)-th, π(1)-th, . . ., π(m−1)-th bit groups or column groups.

A shortening pattern will be described in detail using Table 4 below, byway of example.

TABLE 4 π(0) π(1) π(2) π(3) 2 1 3 0

If input information bits are u={1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1} with(K₁=16), parity check matrix have parameters of N₁=24, and M₁=4, and anumber of information bits to be obtained by shortening is 6, then anumber of information bits to be shortened is 10. Because the number ofcolumn groups (K₁/M₁) is 4, a number of bit groups is 4. So, theinformation bits may be expressed as u ₀={1 0 0 1}, u ₁={1 0 0 0}, u₂={1 1 1 0}, and u ₃={1 0 0 1}.

The number of bit groups in which all bits should be shortened is 2because the number of information bits to be shortened is 10 and eachbit group has 4 bits. Therefore, as shown in Table 4, shortening isperformed on information bits corresponding to a third bit group u ₂since π(0)=2, and shortening is performed on information bitscorresponding to a second bit group u ₁ since π(1)=1. Additionally,because there are two more bits as information bits to be shortened,only two bits among information bits corresponding to a fourth bit groupu ₃ are shortened based on π(2)=3.

In conclusion, the results obtained by shortening the information bits u₀={1001}, u ₁={1000}, u ₂={1110}, and u ₃={1001} are u ₀={1001}, u₁={0000}, u ₂={0000}, and u ₃={0001}. That is, bits {1 0 0 1 0 0 0 0 0 00 0 0 0 0 1} are obtained by shortening input information bits u={1 0 01 1 0 0 0 1 1 1 0 1 0 0 1}.

FIG. 11 illustrates an encoding operation of an LDPC encoder accordingto an embodiment of the present invention. Specifically, FIG. 11illustrates a method for generating an LDPC code having a differentcodeword length or code rate using a given parity check matrix of anLDPC code.

In step 1101, an LDPC encoder 611 reads information about a parity checkmatrix of an LDPC code for shortening, or information such as weight-1position sequences. Thereafter, the LDPC encoder 611 performs shorteningaccording to a required length of an information word of an LDPC codebased on the read information about a stored parity check matrix,through a shortening process including Shortening Steps 1-3, in steps1103 to 1115.

Shortening Step 1: In step 1103, the LDPC encoder 611 determines whetherK_(2,BCH) is less than or equal to 360. Based on the determinationresults, the LDPC encoder 611 calculates a value of m for determining anumber of bit or column groups to be shortened according to the lengthK_(2,BCH) of an information word, after being shortened, as shown inTable 1, in steps 1105 and 1107. Specifically, when K_(2,BCH) is lessthan or equal to 360, m is calculated using K₁/M₁−1 in step 1105, andwhen K_(2,BCH) is not less than or equal to 360,

$m = \left\lfloor \frac{K_{BCH} - K_{2,{BCH}}}{M_{1}} \right\rfloor$

in step 1107.

Shortening Step 2: The LDPC encoder 611 selects sequences for (m+1) bitor column groups according to Table 2 or 3, and shortens all bit orcolumn groups corresponding to the first m sequences, in steps 1109 and1111.

Shortening Step 3: The LDPC encoder 611 applies additional shortening toinformation bits in the remaining (m+1)-th bit or column group, orcorresponding columns in the column group according to the value of m,as shown in Table 1, in steps 1113 and 1115.

In step 1117, the LDPC encoder 611 generates a codeword through LDPCencoding. Thereafter, if puncturing is required, the LDPC encoder 611applies puncturing to the LDPC codeword in step 1119.

In accordance with an embodiment of the present invention, before step1103, shortening or puncturing patterns may be determined differentlyaccording to a ratio of a number of shortened bits to a number ofpunctured bits.

FIG. 12 is a block diagram illustrating a transmission apparatus using ashortened LDPC code according to an embodiment of the present invention.

Referring to FIG. 12, the transmission apparatus includes a controller1210, a shortening pattern applying unit 1220, an LDPC code's paritycheck matrix extractor 1240, an LDPC encoder 1260, and optionallyincludes a puncturing pattern applying unit 1280.

The LDPC code's parity check matrix extractor 1240 extracts a paritycheck matrix of an LDPC code, to which shortening is to be applied. TheLDPC code's parity check matrix may be extracted using a memory, may begiven in the transmission apparatus in advance, or may be directlygenerated in the transmission apparatus.

The controller 1210 controls the shortening pattern applying unit 1220to determine a shortening pattern according to a length of aninformation word and a ratio of a number of bits to be shortened to anumber of bits to be punctured. The shortening pattern applying unit1220 inserts bits with a value of 0 or 1 in positions corresponding toshortened bits, or removes columns corresponding to shortened bits in agiven parity check matrix of an LDPC code or uses only the columns whichdo not correspond to the shortened bits.

The shortening pattern may be determined by using a shortening patternstored in a memory, by generating a shortening pattern using a sequencegenerator (not shown in the drawing), or by using a density evolutionanalysis algorithm for a parity check matrix and a given length of aninformation word.

The shortening pattern applying unit 1220 may apply a differentshortening pattern according to a ratio of a number of shortened bits toa number of punctured bits, or to a code rate. Examples of shorteningpatterns determined according to the ratio of the number of shortenedbits to the number of punctured bits are listed in Tables 2 and 3.

The shortening pattern applying unit 1220 may apply a differentshortening pattern to a specific region having a different ratio of anumber of shortened bits to a number of punctured bits, or a differentcode rate.

The LDPC encoder 1260 performs encoding based on the LDPC code shortenedby the controller 1210 and the shortening pattern applying unit 1220. Ifapplication of appropriate puncturing is required, the puncturingpattern applying unit 1280 applies puncturing to the LDPC codewordgenerated by the LDPC encoder 1260.

FIG. 13 is a block diagram illustrating a reception apparatus using ashortened LDPC code according to an embodiment of the present invention.Specifically, the reception apparatus illustrated in FIG. 13 receives asignal transmitted from a communication system using the shortened LDPCcode, and restores user-desired data from the received signal bydetecting a length of the shortened LDPC code and a ratio of a number ofshortened bits to a number of punctured bits, from the received signal.

Referring to FIG. 13, the reception apparatus includes a controller1310, a shortening/puncturing pattern determiner 1320, a demodulator1330, and an LDPC decoder 1340.

The demodulator 1330 receives and demodulates a shortened LDPC code, anddelivers the demodulated signal to the shortening/puncturing patterndeterminer 1320 and the LDPC decoder 1340.

The shortening/puncturing pattern determiner 1320, under control of thecontroller 1310, estimates or determines information about a shorteningor puncturing pattern of the LDPC code from the demodulated signal, anddelivers position information of the shortened and/or punctured bits tothe LDPC decoder 1340. The shortening/puncturing pattern determiner 1320may deliver information about different patterns to the LDPC decoder1340 according to a ratio of a number of shortened bits to a number ofpunctured bits.

The shortening/puncturing pattern determiner 1320 may determine orestimate a shortening or puncturing pattern by using a shorteningpattern stored in a memory, by generating a shortening pattern using asequence generator (not shown in the drawing), or by using a densityevolution analysis algorithm for a parity check matrix and a givenlength of an information word. The shortening/puncturing patterndeterminer 1320 may determine a different shortening or puncturingpattern according to the ratio of the number of shortened bits to thenumber of punctured bits.

The LDPC decoder 1340 restores user-desired data from the receivedsignal using a length of the shortened/punctured LDPC code and positionsof the shortened/punctured bits determined by the shortening/puncturingpattern determiner 1320.

FIG. 14 illustrates a reception operation in a reception apparatusaccording to an embodiment of the present invention.

Referring to FIG. 14, in step 1401, the demodulator 1330 receives anddemodulates a shortened LDPC code. In step 1403, theshortening/puncturing pattern determiner 1320 determines or estimates ashortening or puncturing pattern based on a ratio of a number ofshortened bits to a number of punctured bits of the demodulated signal,or on a code rate. The shortening/puncturing pattern determiner 1320 maydetermine or estimate a different shortening or puncturing pattern for aspecific region having a different ratio of the number of shortened bitsto the number of punctured bits, or a different code rate.

In step 1405, the shortening/puncturing pattern determiner 1320determines whether there are shortened/punctured bits.

If there are no shortened/punctured bits, the LDPC decoder 1340 performsdecoding in step 1411. However, if there are shortened/punctured bits,the shortening/puncturing pattern determiner 1320 delivers positioninformation of the shortened/punctured bits to the LDPC decoder 1340 instep 1407.

The LDPC decoder 1340 determines that a probability that values of theshortened bits will be 0 is 1, based on the position information of theshortened/punctured bits, and determines that the punctured bits areerased bits, in step 1409. Thereafter, the LDPC decoder 1340 performsLDPC decoding in step 1411.

As is apparent from the foregoing description, according to thedescribed embodiments of the present invention, LDPC codewords havingvarious codeword lengths or code rates can be generated using shorteningand a parity check matrix given in a communication system using an LDPCcode.

In addition, in accordance with an embodiment of the present invention,a shortening pattern is designed based on a ratio of a number ofinformation bits to be shortened to a number of bits to be punctured,thereby supporting suboptimal performance of a shortened LDPC code.

Accordingly, the above-described embodiments of the present inventioncan optimize encoding/decoding performance using information about aparity check matrix given in a communication system using an LDPC code.

While the present invention has been shown and described with referenceto certain embodiments thereof, it will be understood by those skilledin the art that various changes in form and details may be made thereinwithout departing from the spirit and scope of the present invention asdefined by the appended claims and their equivalents.

What is claimed is:
 1. A method for channel encoding in a communicationsystem using low-density parity check (LDPC) codes having differentcodeword lengths and a parity check matrix by performing at least one ofshortening or puncturing, the method comprising: encoding input bitsusing a Bose-Chaudhuri-Hocquenghem (BCH) code; shortening one or morebits of the encoded input bits according to a number of bit groups to beshortened and an order among a plurality of orders according to whichthe bit groups are shortened, wherein the number of bit groups to beshortened is based on a number of bits to be shortened which is based ona number of the encoded input bits; encoding information bits includingthe encoded input bits and the shortened one or more bits, using an LDPCcode to generate parity bits; puncturing one or more bits in the paritybits based on a puncturing parameter among puncturing parameters; andtransmitting a signal that is generated from the encoded informationbits based on the punctured one or more bits, wherein the plurality oforders are based on the puncturing parameters and include a first orderand a second order that is different from the first order.
 2. The methodof claim 1, wherein if a length of an LDPC codeword is 16200, a lengthof the information bits is 3240, and the first order is applied, thenshortening is performed on 7th, 6th, 3rd, 5th, 2nd, 4th, 1st, 8th, and0th groups among the bit groups, in order; and if the length of the LDPCcodeword is 16200, the length of the information bits is 3240, and thesecond order is applied, then shortening is performed on the 7th, 3rd,6th, 5th, 2nd, 4th, 1st, 8th, and 0th groups among the bit groups, inorder.
 3. The method of claim 1, wherein the puncturing parametersinclude a ratio of a number of the punctured one or more bits to anumber of the shortened one or more bits.
 4. An apparatus for channelencoding in a communication system using low-density parity check (LDPC)codes having different codeword lengths and a parity check matrix byperforming at least one of shortening or puncturing, the apparatuscomprising: at least one processor configured to: encode input bitsusing a Bose-Chaudhuri-Hocquenghem (BCH) code, shorten one or more bitsof the encoded input bits according to the of bit groups to be shortenedand an order among a plurality of orders according to which the bitgroups are shortened, wherein the number of bit groups to be shortenedis based on a number of bits to be shortened which is based on a numberof the encoded input bits, encode information bits including the encodedinput bits and the shortened one or more bits using an LDCP code togenerate parity bits, and puncture one or more bits in the parity bitsbased on a puncturing parameter among puncturing parameters LDPC-encodedinformation bits; and a transmitter configured to transmit a signal thatis generated from the encoded information bits based on the puncturedone or more bits, wherein the plurality of orders are based onpuncturing the parameters and include a first order and a second orderthat is different from the first order.
 5. The apparatus of claim 4,wherein if a length of an LDPC codeword is 16200, a length of theinformation bits is 3240, and the first order is applied, thenshortening is performed on 7th, 6th, 3rd, 5th, 2nd, 4th, 1st, 8th, and0th groups among the bit groups, in order; and wherein if the length ofthe LDPC codeword is 16200, the length of the information bits is 3240,and the second order is applied, then shortening is performed on the7th, 3rd, 6th, 5th, 2nd, 4th, 1st, 8th, and 0th groups among the bitgroups, in order.
 6. The apparatus of claim 4, wherein the puncturingparameters include a ratio of a number of the punctured one or more bitsto a number of the shortened one or more bits.
 7. A method for channeldecoding in a communication system using low-density parity check (LDPC)codes having different codeword lengths and a parity check matrix byperforming at least one of shortening or puncturing, the methodcomprising: receiving, from a transmitter, a signal that is generatedfrom encoded information bits, based on punctured one or more bits; anddecoding data in the received signal, wherein the encoded informationbits are generated by encoding, using an LDPC code to generate paritybits, information bits including encoded input bits using aBose-Chaudhuri-Hocquenghem (BCH) code and shortened one or more bits,wherein the punctured one or more bits are punctured in the parity bitsbased on a puncturing parameter among puncturing parameters, wherein theone or more bits are shortened according to a number of bit groups to beshortened and an order among a plurality of orders according to whichthe bit groups are shortened, wherein the number of bit groups to beshortened is based on a number of bits to be shortened, which is basedon a number of the encoded input bits, and wherein the plurality oforders are based on the puncturing parameters and include a first orderand a second order that is different from the first order.
 8. The methodof claim 7, wherein if a length of an LDPC codeword is 16200, a lengthof information bits is 3240, and the first order is applied, then 7th,6th, 3rd, 5th, 2nd, 4th, 1st, 8th, and 0th groups are determined asshortened, in order; and wherein if the length of the LDPC codeword is16200, the length of the information bits is 3240, and the second orderis applied, then the 7th, 3rd, 6th, 5th, 2nd, 4th, 1st, 8th, and 0thgroups are determined as shortened, in order.
 9. The method of claim 7,wherein the puncturing parameters include a ratio of a number of thepunctured one or more bits to a number of the shortened one or morebits.
 10. An apparatus for channel decoding in a communication systemusing low-density parity check (LDPC) codes having different codewordlengths and a parity check matrix by performing at least one ofshortening or puncturing, the apparatus comprising: a receiverconfigured to receive, from a transmitter, a signal that is generatedfrom encoded information bits, based on punctured one or more bits; andat least one processor configured to decode data in the received signal,wherein the encoded information bits are generated by encoding, using anLDPC code to generate parity bits, information bits including encodedinput bits using a Bose-Chaudhuri-Hocquenghem (BCH) code and shortenedone or more bits, wherein the punctured one or more bits are puncturedin the parity bits based on a puncturing parameter among puncturingparameters, wherein the one or more bits are shortened according to anumber of bit groups to be shortened and an order among a plurality oforders according to which the bit groups are shortened, wherein thenumber of bit groups to be shortened is based on a number of bits to beshortened, which is based on a number of the encoded input bits, andwherein the plurality of orders are based on the puncturing parametersand include a first order and a second order that is different from thefirst order.
 11. The apparatus of claim 10, wherein if a length of anLDPC codeword is 16200, a length of information bits is 3240, and thefirst order is applied, then 7th, 6th, 3rd, 5th, 2nd, 4th, 1st, 8th, and0th groups are determined as shortened, in order; and wherein if thelength of the LDPC codeword is 16200, the length of the information bitsis 3240, and the second order is applied, then the 7th, 3rd, 6th, 5th,2nd, 4th, 1st, 8th, and 0th groups are determined as shortened, inorder.
 12. The apparatus of claim 10, wherein the puncturing parametersinclude a ratio of a number of the punctured one or more bits to anumber of the shortened one or more bits.